Geostationary orbits and Lagrange points

Geostationary orbit

What if you could park a satellite in a permanent position so it moves along with the Earth? How useful would that be?

Most satellites are in a dynamic orbit around the Earth. You can see then after sunset and before sunrise, moving like a silent aeroplane through the sky.

This photo shows one. My daughter and I were trying to get a photo and a satellite photobombed the Pleiades. This happens a lot.

Because these satellites move in relation to the Earth, they can look down and see large parts (in some cases the whole) of the Earth slip by underneath them. It's useful for spy satellites, weather satellites, and GPS satellites. Communication satellites are like mobile phone towers, in that you can swap from one to another without breaking the call.

But having satellites that don't move in relation to the Earth, that just hang in one place, is terribly useful. You've seen all those TV dishes on people's houses - they don't track at all, but simply stare at one unmoving point. Much cheaper and simpler. So-called geostationary satellites orbit above the equator at exactly 35,786km, an area called the Clarke Belt. Higher than that, the satellite appears to move backwards from the ground, and lower than that it moves forwards.

This narrow ring above the equator is getting very crowded. Some countries have taken to tilting the orbit slightly, allowing the satellites to shuffle around in the ring. This helps a bit, but there's still the risk of a (fairly gentle) collision, and from the ground the satellite seems to wobble about in a figure-eight shape. This may or may not be a problem depending on your TV dish.

Dead satellites are also a problem. If the operator can't move the satellite out of the way, it turns into space junk.

But what if you could park a satellite - even a really big one like a space station - in a distant, permanent position so it moves with the Earth and never has to be repositioned? How useful would that be?

Lagrange points

Geostationary orbits are useful. But what if you could park a satellite in a distant, permanent position so it moves with the Earth and never has to be repositioned? How useful would that be?

There's another group of "stationary" places that a satellite might be parked. These are called "Lagrange points". Every pair of orbiting bodies (like a planet and the Sun) has five of these points. Here, gravity and centripetal forces and the Coriolis effect are exactly balanced.

(I'm not going to get too detailed because, frankly, I can't!)

L1, L2 and L3

Lagrange 1 (L1) between the Earth and the Sun is about 1 per cent of the way to the Sun in a direct line from Earth. L2 is the same distance away from the Earth in the opposite direction, so it's always in the Earth's shadow.

L3 is on the other side of the sun, exactly at Earth's distance.

These three points are known as "saddles" because anything that finds itself to the left or right of the point are attracted right back again, but anything above or below it are forced further away.

Satellites or space stations parked here would need only a small amount of fuel for orbital adjustments, and with very occasional refuelling you'd be able to stay there for ever. In fact, NASA has a solar observing satellite at L1, and is about to use L2 for the nearly-complete James Webb Space Telescope.

James Webb will always be in the Earth's shadow, because Lagrange point L2 is the ultimate "dark sky site"!

L4 and L5

But what about the other two points, L4 and L5? These two points are along the Earth's orbit, 60 degrees ahead and behind. You can see them in the diagram.

Try as I might, I just can't get my head around these points. My old HSC Physics isn't up to it.

The points are "stable", meaning something just balanced there will stay. However, as soon as it gets shifted (say, by a collision or by solar wind), it falls away. And then the strangeness begins.

If something moves from L4 or L5 towards the Sun, it begins to speed up, meaning it starts to overtake the Lagrange point. Because of this, the centripetal force on the object increases, pushing it back out ahead of the Lagrange point (this is called the Coriolis Effect). Then it passes the original orbit, slowing down again, so it starts to fall back towards the Sun, ending up crossing the original orbit behind the Lagrange point. The shape of the orbit is described as a "kidney bean".

And at about this point my brain decides to go and have a little lie down somewhere.

It was hard to find, but NASA photographed an asteroid orbiting Earth's L4, the leading point. It's only 150-500m in size, and was named 2010 TK7. You can see it as a tiny speck in the photo - in the small green circle. Apart from a cloud of dust, there doesn't appear to be anything at Earth's L5 point.

However, there are heaps of asteroids at other L4 and L5 points elsewhere in the solar system. Neptune, in particular has lots. There are even tiny lumps in Lagrange points between Saturn's moons. They're all over the place.

(Photos and graphic: NASA)